Autonomous University of Barcelona
Autonomous University of Barcelona &
Kozminski University
Autonomous University of Barcelona
2023-05-02
NSUM = Survey instrument + Statistical model
Classic (Killworth et al. 1990)
How many people do you know who are members of [subpopulation]?
Dichotomous (Baum and Marsden 2023)
Do you know anyone who is a member of [subpopulation]?
BRIDGES survey
Now I will ask you about the people you know in Spain in general. I will ask about the people you know with certain characteristics. By knowing someone we understand that you know the first name of this person and you would recognize one another if you ran into them for example in the street, in a shop, or in another place. This includes both close relationships such as your partner, family, friends, neighbors, coworker or fellow students and less close relationships, such as for example people whom you have met in the associations to which you belong or who you know via other people.
These people do not have to live near you, you can also be in contact with them through social media or by phone. You may like them or not. Please do not include deceased persons, people under 18 years old, nor yourself.
How many people over the age of 18 do you know (by name and by sight) who have the following jobs, whether they are women or men?
McCormick, Salganik, and Zheng (2010) suggest:
Another area for future methodological work is formalizing the procedure used to select names that satisfy the scaled-down condition. Our trial-and-error approached worked well here because there were only eight alter categories, but in cases with more categories, a more automated procedure would be preferable.
(McCormick, Salganik, and Zheng 2010)
Number of persons in the population with name \(i\) belonging to category \(j\)
\[f_i^j\]
Marginal distribution of traits in population
\[f^j = \sum_{i} f_i^j\]
Marginal distribution of traits in selected subset \(S\) of names
\[\hat{f}^j = \frac{\sum_{i \in S} f^j_i}{\sum_{i \in S} \sum_k f^k_i}\]
\[\arg\min_S \sum_j D(f^j, \hat{f^j})\]
Given the…
… find a subset \(S\) of names for which the selected distance measure \(D(\cdot)\) comparing…
… is as small as possible.
Let
\[\alpha = \frac{1}{\sum_{i \in S} \sum_k f^k_i}\]
then
\[\arg\min_S \sum_j \left(f^j - \alpha \sum_i f^j_i x_i \right)^2\]
where \(x_i=1\) if name \(i\) is in the subset and \(x_i = 0\) otherwise
More info: http://coalesce-lab.com/en
www